PoS(EDSU2018)043. Supergravity and Cosmology

Transcription

1 Supergravity and Cosmology Stanford Institute for Theoretical Physics and Department of Physics Stanford University Stanford CA 90 USA For cosmology we need General Relativity. Supergravity is the next natural step after General Relativity. Superstring theory is believed to be the most fundamental theory we know. However string theory has an emergent concept of space-time. To use it in the context of the - dimensional General Relativity and cosmology requires many intermediate steps. If in these steps some amount of supersymmetry maximal or minimal or intermediate is preserved one finds consequences for cosmology potentially supportable or falsifiable by observations. PoS(EDSU08)0 nd World Summit: Exploring the Dark Side of the Universe -9 June 08 - EDSU08 University of Antilles Pointe-à-Pitre Guadeloupe France Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives.0 International License (CC BY-NC-ND.0).

2 Short Title for header Fundamental idea following the discovery of General Relativity is the idea of local supersymmetry. Einstein s dream of unifying electromagnetism and gravity was realized starting extended N supergravity. The model does so by adding two real gravitino to the photon and the graviton. The first breakthrough into finiteness of quantum supergravity occurred via this unification: an explicit calculation of photon-photon scattering which was known to be divergent in the coupled bosonic Maxwell-Einstein system yielded a dramatic result : the new diagrams involving gravitinos cancelled the divergences found previously. Many more unexpected cancellation of the quantum loop divergences were discovered later in extended maximal supergravities up to N 8 supersymmetries. However supergravity models discovered in 9 linearly realized supersymmetry tend to have an easy descriptions of anti-de Sitter vacua negative cosmological ant. The have difficulty in describing the Universe we see in observations where we need to explain the origin of the positive cosmological ant for example via a de Sitter vacua as well as near de Sitter describing a slow-roll potentials in inflationary cosmology. Cosmology: from the sky to the fundamental physics BK w / 9GHz 0 Moriond // Planck XX 0 If B-modes are discovered soon r > 0 - natural infla;on models axion monodromy models a-a?ractor models will be validated No need to worry about log scale r RK Linde Roest 0 PoS(EDSU08)0 Otherwise we switch to log r to see 0 - < r < 0 - Figure : Planck 0 n s r plane blue area representing the σ data. In this talk we will describe the recently discovered De Sitter supergravity [] nilpotent superfield and based on it inflationary model building. We present inflationary models still consistent Planck 0 [] in n s r plane in Fig.. The models at present compatible the data include the so-called α-attractors [] which we will describe in the context of supergravity. In fact the most advanced geometric version of these models are using de Sitter supergravity a nilpotent multiplet and a Kähler function []. We show the place of these models in Planck 0 n s r plane in Fig.. We explain the geometric nature of these models in Fig.. The main feature of these models is a particular choice of the moduli space which is a Poincaré disk. There is a corresponding Escher s picture where R Escher α.

3 Short Title for header We will explain the new M-theory/String theory inspired targets for B-modes beyond the well known satellite targets like R and Higgs inflation r of the order 0. The new targets shown in Fig. below a scan the region of r between 0 and 0.. De Sitter supergravity Standard linear N supersymmetry in four dimensions as discovered by Gol fand and Lichtman in 9 and By Wess and Zumino in 9 was the major paradigm in particle physics for decades. LHC was expected to produce super-partners of known particles one Majorana fermion for each complex scalar and vice versa. So far we have not seen them which of course is easy to explain if the super-partners are heavier than predicted. In any case another issue linear supersymmetry was realized in the context of cosmology. In all linearized supersymmetries N there are theorems under certain conditions supporting anti-de Sitter vacua unbroken supersymmetry and forbidding de Sitter vacua spontaneously broken supersymmetry. Meanwhile starting 998 discovery of the dark energy it become clear that de Sitter space offers a is a simple explanation of the Einstein equations a positive cosmological ant. During the last two decades all data points towards the fact that a positive cosmological ant is still a possible explanation of the cosmological data. The difficulties (in absence of scalar fields) of standard linearized supersymmetry to produce such theories forced us to study a non-linear realization supersymmetry which was in fact discovered long time by Volkov and Akulov in 9. This theory is equivalent to a theory a rained chiral multiplet where only a fermionic degree of freedom is present and a scalar field is a bilinear of the fermion one S (xθ) 0 S(xθ) ψψ(x) F + θψ(x) + θ F (.) To explain a consistency between a positive cosmological ant and supersymmetry it was necessary to promote Volkov-Akulov theory or a theory the nilpotent multiplet to a theory a local supersymmetry. This was done in []. When such a multiplet is present in the action one finds that even in absence of scalar fields such supergravity actions have de Sitter vacua spontaneously broken supersymmetry. In 99 J. Polchinski discovered in string theory the non-perturbative objects called D-branes and a year later it was recognized that the theory of non-linearly realized supersymmetry of the Volkov-Akulov type is a property of the world-volume actions of all D-branes. Therefore it was also recognized that the KKLT uplifting mechanism in string theory is associated a nilpotent multiplet [] and therefore also de Sitter supergravity. PoS(EDSU08)0. α-attractor models These models have an interesting property that the potentials for canonical fields are for T- models and E-models respectively ( V T V 0 tanh φ ) n V E V 0 ( e α ) n α φ (.)

4 regard to initial conditions for inflation analogous to the ones studied in [8] for models out SUSY breaking and dark energy. We close in Section a summary of what we have accomplished. Short Title for header. Review and attraction SL( R) symmetry these forz ds models dzd ( Z Z ) Figure : Planck 0 ns r plane blue area representing the σ data. At sufficiently small α these models have simple observables ns N r α N (.) Here N is the number of e-foldings. In Fig. there is a T-model n shown by two yellow lines for N 0 and N 0. All α-attractor models are inside σ for ns and waiting for the discovery of primordial gravitational waves or new bounds on r to identify the value of α. In Fig. we explain some of the properties of these models in geometric terms. The T-models in geometric variables have a non-canonical kinetic term defined by the metric of a Poincaré disk and for example the n potential is very simple just Z Z.. New B-mode targets The region of r between between 0 and 0 is expected to be a playground for the satellite B-mode missions. In the context of α-attractor cosmological models the value of α can be arbitrary as long as we only consider the embedding of the models in (.) into phenomenological N supergravity. The value of α R K related to the curvature of the Kähler manifold RK as shown in Fig. is not restricted it can take any value. However it was recently discovered in [] that if one derives the corresponding kinetic terms starting from the maximal supersymmetry: M-theory in d superstring theory in d0 N 8 supergravity in d the situation changes. Only integer values of α are possible. We have shown the corresponding values of r according to (.) in the Fig.. These seven targets correspond to Escher s disks of REscher. PoS(EDSU08)0 There is a key parameter in which the Ka hler ln(t + T ). It ds potential dt dt K (T + T ) describes the moduli space curvature [9] given by RK. Another also geometric interpretation Curvature of the moduli space in Kahler of this parameter is in terms of the Poincare disk model of a hyperbolic the radius Z Z < p Hyperbolic illustrated by the Escher sof apicture Circle Limit IV [ ]. As clarified in these references Poincaré disk T + T > 0 Disk or half-plane from the fundamental point of view there are particularly interesting values of depending on the Escher in the Sky RK Linde 0 original theory. From the maximal N superconformal theory [] one would expect / r 0. This corresponds to the unit radius Escher disk [] as well as a target of the REscher 0 r future space mission for B-mode detection as specified in CORE (Cosmic ORigins Explorer). Some interesting simplifications occur for /9 which corresponds to the GL model [89]. From N

5 a Short Title for header r 0- T E Seven new targets 0- N r N Figure : The CMB-S figure represents the ns r plane for the future data. The grey band shows one of the Figure : This Figure taken [] ittargets represents forecast of CMB-Sand raints in the The ns seven r plane α-attractor models. Oneiscan seefrom the orange thereafor the Starobinsky Higgs models. fornew a fiducial colors r 0.0. the grey shows predictions the sub-class targetsmodel at various scan Here the region of rband between 0 and 0 of which is expected to be probedmodels by [ ]. We have added to this figure a blue circle the letter T inside it corresponding to a highest the satellite missions. These targets are derived from M-theory/String theory. preferred value and the purple one corresponding to the lowest preferred value in a seven-disk. All intermediate cases { p } are between these two. They all describe the class models V tanh ('/ ) so-called quadratic T -models. The quadratic E-models p V ( e / ' ) tend to be slightly to the right of the T -models see []. We show them as a navy circle References the letter E inside it. [] E. A. Bergshoeff D. Z. Freedman R. Kallosh and A. Van Proeyen Phys. Rev. D 9 no (0) Erratum: [Phys. Rev. D 9 no (0)] doi:0.0/physrevd /PhysRevD [arxiv:0.08 F. Hasegawa and Y. Yamada : [hep-th]]. Component action of nilpotent multiplet coupled to matter in dimensional supergravity : N JHEP 0 0 (0) doi:0.00/jhep0(0)0 [arxiv:0.089 [hep-th]]. : by requiring that : Collaboration] Planck 0 results. XX. Constraints [] P. A. R. Ade et al. [Planck on inflation Astron. A0 : doi:0.0/000-/0898 Astrophys. 9 (0) [arxiv:0.0 [astro-ph.co]]. : [] R. Kallosh A. Linde and D. Roest Superconformal Inflationary α-attractors JHEP (0) : (.) R. 98 doi:0.00/jhep(0)98 [arxiv:.0 [hep-th]]. M. Galante Kallosh A. Linde and D. Roest Unity of features Cosmological Inflation Attractors Lett. the (0) no. We illustrate in Fig. the models Phys. [ Rev. ] seven-disk 0 doi:0.0/physrevlett..0 [arxiv:.9 [hep-th]]. J. J. M. Carrasco using the recent discussion of B-modes in the CMB-S Science Book []. We show in Fig. R. Kallosh A. Linde and D. Roest Hyperbolic of cosmological D for predictions models seven-disk in the ns attractors r plane Phys. for NRev. 9 no. 00 (0) doi:0.0/physrevd.9.00 [arxiv:0.0 [hep-th]]. the minimal value and for the maximal value. [] R. Kallosh A. Linde D. Roest and Y. Yamada D induced geometric inflation JHEP 0 0 (0) doi:0.00/jhep0(0)0 [arxiv:0.09 [hep-th]]. Values of in string theory [] R. Kallosh and T. Wrase Emergence of Spontaneously Broken Supersymmetry on an Anti-D-Brane in KKLT ds Vacua the -disk (0) doi:0.00/jhep(0) Here we will show how JHEP to derive (.) in string [arxiv:. theory. We start [hep-th]]. E. Bergshoeff K.symmetries Dasgupta R. in Kallosh Van Proeyen and T. [] Wrase[8]. D and the derivation of A. non-compact stringa.theory following ThedS toroidal JHEP 0 08 (0) doi:0.00/jhep0(0)08 [arxiv:0.0 [hep-th]]. [] S. Ferrara and R. Kallosh Seven-disk manifold α-attractors and B modes Phys. Rev. D 9 no. 0 (0) doi:0.0/physrevd.9.0 [arxiv:0.0 [hep-th]]. R. Kallosh A. Linde T. Wrase and Y. Yamada Maximal Supersymmetry and B-Mode Targets JHEP 0 (0) doi:0.00/jhep0(0) [arxiv:0.089 [hep-th]]. PoS(EDSU08)0 ns T